Geothermal air vs water – The math

Math is hard… especially in complex systems. Therefore what I’m about to do may have errors. There may be holes in my understanding. Hopefully, if you see an error or hole, you’ll let me know. Here goes…

Air holds less energy than water. About 4 times less. That means that you can sink lots of energy into water without raising its temperature much. Water can also transfer energy (thermal conductivity) better than air. These attributes should make water superior to air at heating or cooling, right? Well, as I have learned, maybe not.

Air contains water. Up to 2% of air is water vapor. How many grams of water per cubic meter of air depends on the air’s temperature. The warmer the air is, the more water it can hold. For example, one cubic meter of air (1.2kg) at 30C can contain 30g of water at 100% saturation or 100% humidity. At 15C, air only can hold 12g of water (again at 100% humidity). I’ll be using those temperatures later in my examples, so take note.

Latent heat

When water changes from a liquid state, to a gas state (and vice-versa), it takes a certain amount of energy. It takes 2257 joules per gram of liquid water to change it from a liquid to gas. In my understanding, the energy to phase change the water will come from the warmest available source. In a geothermal cooling situation, the energy is going to come from the air because it’s warmer. We can calculate, then, how much energy will be taken out of the air as it goes from one temperature to another. We can estimate a best-case energy transfer air to a 15C geothermal thermal mass. I compiled the following chart showing the best-case performance of geothermal air per humidity level:

From the chart, we can see that it’s possible to condense 100% of the available air above 50% humidity. We also see that we move about 18,000 joules of energy from the air during this transfer. By contrast, taking the same mass of water (1.2kg) from 30C to 15C without any phase changes transfers 75,312 joules. Even with the latent bonus, more energy is being transferred with water.

The devil is in the details. How quickly can you transfer that amount of energy using the various mediums and what is the cost are really the questions. How likely is it that you will be able to achieve a water temperature shift from 30C to 15C? I guess it depends on the amount of tubing in the ground. Likewise, we are making assumptions about the air system -that all available water has been condensed and the humidity of the air coming out is almost 100%.

Update (2016/10/24): I originally claimed the air coming out would be 0%. That is incorrect since not all the water vapor will be condensed.

Too make the muddy water less clear, a geothermal water system isn’t exactly 100% sensible (no phase changes). For example, I see water condensing around my heat exchanger. Water can also condense around the reservoir surface area but I have not noticed it (nor have I looked for it). This condensing effect might be just as good as a geothermal air system, but I don’t have the proper tools to test it and my temperatures are probably not warm enough to do the testing until next year anyway. So we’ll have to leave that as an open question: does the latent effects of a water system with heat exchanger equal that of a geothermal air system?

Heating

Air is probably better at cooling than it will be at heating. The main reason is that the amount of moisture that the air can hold at cool temperatures is low. If you live in an area like mine where the cool months still have high humidity, this effect is reduced even more because there just won’t be the excess capacity in the air to hold any water vapor. Without water vaporizing or condensing, there will be no latent heating bonus.

I put together a similar chart showing, again, best-case results where the air picks up as much moisture from the soil as possible (achieving 100% humidity every pass). I’m assuming that air that wicks up moisture gains the energy from the phase change of liquid from the soil to gas. I started with an air temperature of 0C and a geothermal mass of 10C.

How does that compare to water? Well, to take 1.2kg of 0C water to 10C takes 51000 joules of energy (ignoring phase change). That’s enough to warm the air to “7.2C” over 50 times. At one complete exchange of the loop per minute, it will take about 22 hours for the water to achieve that temperature.

Costs

The up front costs of geothermal air are higher than geothermal water. For 200 meters of corrugated 6 inch tubing, the cost is around $500 dollars. For the same length of 1/2″ PEX tubing, it will cost less than $200 dollars. The blower is also more expensive than the pump. Below I’ve listed prices I found for both systems:

What about runtime costs? The pump consumes around 70W. This dayton blower consumes above 200W at full speed. The fan on the heat exchanger runs at about 90W. So even though the water system has more components, the total sum of components uses less power than the air system.

Utility

Utility is how useful a thing is. If it has more than one uses, the better. Are there multiple uses for the air we can take advantage of? Yes. We can use the cool air from the geothermal system to cool lighting such as LEDs but we need extra fans. Ambient air cooling will probably not be adequate. Channeling the air might also be difficult.

Water will have much more utility. Water is going to be better for spot cooling things and for moving energy around. The tubing is much smaller and cheaper and pumps are less expensive. You can use the same pump for the entire system where with air, multiple fans are requires for spot applications. The costs add up. We can easily use a water system to spot cool CO2 generators, lights, and virtually anything else we need to without any additional moving parts or electrical components (generally just tubes and adapters).

Conclusion

Geothermal with air as a medium might be better than water at cooling if water has no latent effects. If water does have latent effects and if latent effects are equal, water is probably better due to it’s capacity to store energy.

The latent effects of air for cooling are diminished in dry environments when air is below 50% humidity. Humidity in high desert states like Utah may not get over 30% during summer days.

For heating, the endothermic bonus for air is not great and since it cannot be used as thermal mass, water could be better.

Temperature stability is going to be better with water because the required amount of energy to change the water’s temperature is greater.

Utility is also better for water because it can be used to spot cool virtually anything without adding additional costs relative to trying to spot cool with air.